Arms which pivot in the vertical plane and are only supported in one place are well known and often used mechanisms. They can be just single arms lifting something at their distal ends or systems of multi-segment linkages, made up of several arms, each one pivotably linked but independently rotatable relative to the other in the vertical plane. In every case where the center of mass is not directly below (or above) the pivot point (and except where there is no force due to gravity) there is a moment about the pivot due to gravity. This tends to make the arm droop downwards and additional effort or energy is necessary to counteract or compensate for this.
A simple way of counteracting the moment due to gravity is by way of a counterweight. A first mass at one end of an arm is balanced by a second mass at the other end. The size of the second mass depends on the relative distances of the two masses to the pivot point. The problem with this is that it either at least doubles the space used or at least adds a mass to the system equivalent to the first mass.
FIG. 1 shows an alternative approach to gravity compensation. A mass 2 having a weight W0 acts at the end of an arm 4, a length L0 from a pivot point 6. It is compensated by a spring 8 acting on a circular surface portion centered on the pivot point 6, a distance R0 therefrom. The spring provides a tension T0 to the circular surface portion, thereby effecting a moment on the arm 4. For the moment due to the spring to compensate the moment due to gravity at any point:T0*R0=W0*L0*Cos A, Where A is the angle of the arm 4 to the horizontal.
As R0, W0 and L0 are constants, this means that T0 must vary with CosA. Therefore it is not a linear spring. The type of spring required is known as a non-linear negative spring, and a satisfactory one has yet to have been developed.
The counterweight and spring approaches are passive approaches. Active ones are known, based on sensors and actuators, but they add very much to the cost and complexity of a device.
The problem of gravity is exacerbated in multi-segment linkages, where several arms are connected together, each one pivotably linked but independently rotatable relative to the other in the vertical plane. Examples of machines which typically might include multi-segment linkages are robotic arms, manipulators, end effectors, three-dimensional measurement arms, lifting assist equipment, surgical scope holders, medical prosthetics, amongst other machines that operate with at least two degrees of freedom.
FIG. 2 shows a system 10 with a base 12 pivotably supporting one end of a first arm 14 at a first joint 16, which first arm pivotably supports a second arm 18 at its other end, at a second joint 20. The second arm 18 itself supports a load 22 at its distal end.
The moments about the first joint 16 are a function of the mass of the first arm 14, the angle of rotation of the first arm 14, and the mass of the second arm 18 and its load 22 and the angle of rotation of the second arm 18. The moments about the second joint 20 are a function of the mass of the second arm 18 and its load 22 and the angle of rotation of the second arm 18.
Thus for the second arm 18 and the load to be gravity compensated, the solution is to produce an external counteracting moment that is exactly the same in magnitude and opposite in direction to the moment about the second joint 20. For the first arm 14 to be gravity compensated, the solution is more complex and needs to take into account the coupled behavior of the whole system. Any counteracting moment at joint 1 will have to consider not just rotation about the first joint 16 but also the rotation about the second joint 20.
In the lower base joints of serial configuration robots, the force used to hold arms and move them against gravity can account for at least 50% of the work provided by the motors, leaving only 50% to do the useful work of moving the robot arm. This is very wasteful.
Published patent document WO 92/05016 describes gravity compensation using an eccentric pulley. The pulley is mounted on the pivot point of an arm and rotates with it. A compliant tendon, acting as a spring, is looped over the pulley. The eccentric pulley is designed to translate the linear spring behavior of the tendon into a nonlinear compensation torque. It is indicated that the approach can work for a multi-segment linkage, but it is not clear how this is achieved.
The present invention is intended to provide an original and inventive approach to passive gravity compensation.